Statistical Power for the Comparative Regression Discontinuity Design With a Pretest No-Treatment Control Function: Theory and Evidence From the National Head Start Impact Study

Yang Tang and Thomas D. Cook

Evaluation Review, 2018, vol. 42, issue 1, 71-110

Abstract: The basic regression discontinuity design (RDD) has less statistical power than a randomized control trial (RCT) with the same sample size. Adding a no-treatment comparison function to the basic RDD creates a comparative RDD (CRD); and when this function comes from the pretest value of the study outcome, a CRD-Pre design results. We use a within-study comparison (WSC) to examine the power of CRD-Pre relative to both basic RDD and RCT. We first build the theoretical foundation for power in CRD-Pre, then derive the relevant variance formulae, and finally compare them to the theoretical RCT variance. We conclude from this theoretical part of this article that (1) CRD-Pre’s power gain depends on the partial correlation between the pretest and posttest measures after conditioning on the assignment variable, (2) CRD-Pre is less responsive than basic RDD to how the assignment variable is distributed and where the cutoff is located, and (3) under a variety of conditions, the efficiency of CRD-Pre is very close to that of the RCT. Data from the National Head Start Impact Study are then used to construct RCT, RDD, and CRD-Pre designs and to compare their power. The empirical results indicate (1) a high level of correspondence between the predicted and obtained power results for RDD and CRD-Pre relative to the RCT, and (2) power levels in CRD-Pre and RCT that are very close. The study is unique among WSCs for its focus on the correspondence between RCT and observational study standard errors rather than means.

Keywords: quasi-experimental design; methodology; methodological development; content area; education; content area (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:sae:evarev:v:42:y:2018:i:1:p:71-110

DOI: 10.1177/0193841X18776117

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